Thanks, Soroban, for making it clear that there are 8 unknown values. I was having trouble counting them because I couldn't keep them straight in my mind.

hoppingmad, as Soroban said, you cannot solve 6 equations for 8 unknown values. But you could solve for 6 of them "in terms of the other two". That is, treat two of them as constants (I don't think it matters which two) and solve the for the other six equal to formulas involving those 2. Exactly how you write the answer depends on exactly what the question is!

Note:
sum of elements in any row equal the sum of elements in corresponding column
Green light times are given as fractions of a minute (1/2 means 30 seconds etc.)
No U turns allowed (S-S = 0 etc.)
4 possible traffic flows are shown below (this is the example given to us sort of showing us how to solve.):

I suppose I'm on the wrong path. please, if it's blatantly obvious where I'm screwing up, a hint in the right direction, I'm working hard on this but I keep hitting a brick wall. There has to be a better way than trial and error right?
I need to find the correct traffic flows...